WASHINGTON – Rep. Rick Lazio yesterday denied he’d asked for the OK to vote against the GOP’s budget to help in his Senate race against Hillary Clinton – although he refused to say how much of it he’ll back.

“I never had any discussion with any member of [Republican] leadership,” Lazio said. “This is an absolute denial.”

“There is no truth whatsoever,” added Lazio, rejecting reports that he wants leaders on the ongoing budget battle to spare him attacks by Clinton.

But Lazio refused to say if he’ll even back one of the 14 separate budget bills working their way through the House, which cut safety and education programs that are popular with many New Yorkers.

Last week, Lazio deserted the Republican Party on two votes.

He said “no” to the $352 billion GOP budget bill for the departments of Education, Labor and Health & Human Services.

Lazio also skipped the vote on the $14 billion Interior Department budget bill, enabling him to effectively say no, although in both cases, the Republicans had enough votes to pass the bill without his backing.

It is common for party leaders, Democrats and Republicans alike, to give lawmakers in close races a green light to vote against the party line if they need to.

The Long Island Republican also said he’s ending his open-door policy of talking with reporters in between his congressional duties, citing a need for “order.”

In a brief interview with The Post outside the office of Democratic Leader Richard Gephardt, Lazio said he no longer will speak to reporters unless they first contact his New York press office.

The change is significant because Lazio entered his race against Clinton by promising to be more accessible to reporters, both in New York and in Washington.

“We’re trying to get some order here,” explained Lazio, who since last month had tried to emulate former Republican presidential candidate Sen. John McCain (Ariz.), who talked often and openly with the press.

Dan McLagan, Lazio’s spokesman, yesterday insisted that there was no policy change.

“This is a very open and accessible campaign. Mrs. Clinton has yet to appear on a Sunday talk show,” McLagan said.